The present invention relates to an image processing method, image processing apparatus and MRI (magnetic resonance imaging) apparatus, and more particularly to an image processing method and apparatus for calculating the average value of complex observed signals from an absolute-value image produced by the complex observed signals, an image processing method and apparatus for calculating the variance of complex observed signals from an absolute-value image produced by the complex observed signals, an image processing method and apparatus for performing image filtering based on the variance of complex observed signals calculated from an absolute-value image produced by the complex observed signals, and an MRI apparatus comprising such image processing apparatuses.
In the instant specification, drawing, and claims, the following letters, symbols and italicized letters and symbols will be used interchangeably and have the same meanings:
(1) M and M
(2) N and N
(3) S and S
(4) Ma and Ma
(5) K and K
(6) W and W
(7) δ and δ
(8) ξ and ξ
An image processing method has been proposed which performs image filtering on an image produced by complex observed signals S, comprising:
(1) estimating the variance α2 of noise contained in the complex observed signals S,
(2) calculating the variance δ2 of the complex observed signals S in a proximate region of a pixel of interest; and
(3) comparing the variance α2 of noise contained in the complex observed signals S and the variance δ2 of the complex observed signals S, and if the variance δ2 of the complex observed signals S is equal to or relatively close to the variance α2 of noise, setting a value in which the average value of pixel values of the pixel of interest and the surrounding pixels dominates as the pixel value for the pixel of interest, and if the variance δ2 of the complex observed signals S is relatively far from the variance α2 of noise, setting a value in which the original pixel value dominates as the pixel value for the pixel of interest.
According to such an image processing method, a higher degree of smoothing is applied to a pixel in a region in which the variance δ2 of the complex observed signals S is equal to or relatively close to the variance α2 of noise, i.e., a region containing approximately constant signal components, and a lower degree of smoothing is applied to pixels in other regions, i.e., regions containing varying signal components.
The variance δ2 of complex observed signals S in a proximate region of a pixel of interest is calculated by the following equation, wherein the average value of the complex observed signals S in the region is represented by M, and the number of pixels as N:δ2=Σ(S−M)2/N,in which the average value M is:M=ΣS/N.For example, considering complex observed signals S1=Z∠0°, S2=Z∠120° and S3=Z∠240° as shown in FIG. 10,M=(S1+S2+S3)/3=0.
However, the average value Ma of pixel values |S| on an absolute-value image sometimes has a value different from the average value M of the complex observed signals S. For example, the average value Ma of the absolute values |S| of the complex observed signals S1=Z∠0°, S2=Z∠120° and S3=Z∠240° shown in FIG. 10 is:Ma=(|S1|+|S2|+|S3|)/3=Z≠0.
In other words, the conventional technique has the following problems:
(1) the average value M of complex observed signals S may not be accurately obtained from an absolute-value image produced by the complex observed signals S;
(2) if the average value M of the complex observed signals S is not accurately obtained, the variance δ2 of the complex observed signals S cannot be accurately obtained; and
(3) if the variance δ2 of the complex observed signals S is not be accurately obtained, the image filtering cannot be accurately performed.